Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe

The paper provides one of the first applications of the double bootstrap procedure (Simar and Wilson 2007) in a two-stage estimation of the effect of environmental variables on non-parametric estimates of technical efficiency. This procedure enables consistent inference within models explaining efficiency scores, while simultaneously producing standard errors and confidence intervals for these efficiency scores. The application is to 88 livestock and 256 crop farms in the Czech Republic, split into individual and corporate.

Asymptotic normality of linear functions of concomitants of order statistics

Let T( ) be a linear function of concomitants of order statistics, whereT (·) denotes a statistical functional depending on some distribution function (df)F and is an estimator ofF. Under an auxiliary model approach we consider statistics of the form , where denotes a weighted empirical df and a finite population df (t denotes a triangular array). The results can be used to estimate income inequality in finite populations and especially when the survey is based on some design. The paper was written when the author was working at the Statistical Research Unit, Statistics Sweden, Stockholm, Sweden The research was supported by the Joint Committé of the Nordic Social Research Council.     

Empirical comparisons of some tests of separate families of hypotheses

Summary This paper is devoted to a comparison of the asymptotic tests of separate families of hypotheses proposed byCox [1961, 1962] and byAtkinson [1970]. The adequacy of the asymptotic results for finite samples is investigated and some conclusions reached. An examination of the terms which differentiate the two procedures is made. Empirical simulated results are discussed for cases involving the exponential, the lognormal and the Weibull distributions.

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Zusammenfassung In dieser Arbeit wird ein Vergleich angestellt zwischen den Vorschlägen vonCox [1961, 1962] undAtkinson [1970] über asymptotische Tests separierter Familien von Hypothesen. Die Angemessenheit der asymptotischen Resultate für endliche Proben wird untersucht und einige Folgerungen gezogen. Eine Prüfung der Terme, die die beiden Verfahren differenzieren, wird vorgenommen. Empirisch simultierte Resultate werden distribuiert für Fälle mit exponential, lognormal und Weibull Verteilungen.

     

Approximations of the eigenvalues of the covariance matrix of a first-order autoregressive process

This paper provides explicit estimates of the eigenvalues of the covariance matrix of an autoregressive process of order one. Also explicit error bounds are established in closed form. Typically, such an error bound is given by $\text{ε}{}_{\mathrm{k}}\text{= (}\text{4}\text{(n+1)}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ρ}{}^2\text{sin}\text{(}\text{kπ}\text{(n+1)}\text{)}$, so that the approximations improve as the size of the matrix increases. In other words, the accuracy of the approximations increases as direct computations become more costly.     

Characterizations of distributions via linearity of regression of generalized order statistics

Let X (r, n, m, k), 1 r n, denote generalized order statistics based on an absolutely continuous distribution function F. We characterize all distribution functions F for which the following linearity of regression holds E(X(r+l,n,m,k) | X(r,n,m,k))=aX(r,n,m,k)+b.We show that only exponential, Pareto and power distributions satisfy this equation. Using this result one can obtain characterizations of exponential, Pareto and power distributions in terms of sequential order statistics, Pfeifers records and progressive type II censored order statistics. Received July 2001/Revised August 2002     

Evaluation of inequivalent projections of Hadamard matrices of order 24

Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. It is of practical interest for a given k to know all the inequivalent projections of the design into the k dimensions. In this paper we give all the (combinatorially) inequivalent projections of inequivalent Hadamard matrices of order 24 into k=3,4 and 5 dimensions, as well as their frequencies. Then, we sort these projections according to their generalized resolution, generalized aberration and centered L₂-discrepancy measure of uniformity. Then, we study the hidden projection properties of these designs as they are introduced by Wang and Wu (1995). The hidden projection property suggests that complex aliasing allows some interactions to be estimated without making additional runs.     

Existence of a convex extension of a preference relation

In this paper we say that a preference (i.e. irreflexive) relationP isregular (or aweak order) if both it and its non-comparability relation are transitive; we also say that a preference relationP ^* is aconvex extension of another preference relationP ifP?P ^* holds andP ^* is regular and convex-valued. We prove that a convex extension ofP exists if and only if every non-empty and finite set of alternativesA is not included in the convex hull of ∪ _x∈A P(x).     

Consistency of a nonparametric estimation of a density functional

LetX be a random variable with distribution functionF and density functionf. Let ? and ψ be known measurable functions defined on the real lineR and the closed interval [0, 1], respectively. This paper proposes a smooth nonparametric estimate of the density functional \(\theta = \int\limits_R \phi (x) \psi \left[ {F (x)} \right]f^2 (x) dx\) based on a random sampleX ₁, ...,X _n fromF using a kernel functionk. The proposed estimate is given by \(\hat \theta = (n^2 a_n )^{ - 1} \mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n \phi (X_i ) \psi \left[ {\hat F (X_i )} \right]k\left[ {(X_i - X_j )/a_n } \right]\) , where \(\hat F(x) = n^{ - 1} \mathop \sum \limits_{i = 1}^n K\left[ {(x - X_i )/a_n } \right]\) with \(K (w) = \int\limits_{ - \infty }^w {k (u) } du\) . The estimate \(\hat \theta \) is shown to be consistent both in the weak and strong sense and is used to estimate the asymptotic relative efficiency of various nonparametric tests, with particular reference to those using the Chernoff-Savage statistic.     

Pythagorean generalization of testing the equality of two symmetric positive definite matrices

We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality between two $k$ dimensional symmetric positive-definite matrices $A$ and $B$: the traces of $A{B}^{?1}$ and $B{A}^{?1}$ are equal to $k$ if and only if $A=B$. Using this simple criterion, we introduce a class of omnibus test statistics for equality and examine their null and local alternative approximations under some mild regularity conditions. A preferred test in the class with good omni-directional power is recommended for practical work. Monte Carlo experiments are conducted to explore performance characteristics under the null and local as well as fixed alternatives. The test is applicable in many settings, including GMM estimation, SVAR models and high dimensional variance matrix settings.     

The effect of the regularity of the error process on the performance of kernel regression estimators

This article considers estimation of regression function $f$ in the fixed design model $Y(x_i)=f(x_i)+ \epsilon (x_i), i=1,\ldots ,n$ , by use of the Gasser and Müller kernel estimator. The point set $\{ x_i\}_{i=1}^{n}\subset [0,1]$ constitutes the sampling design points, and $\epsilon (x_i)$ are correlated errors. The error process $\epsilon $ is assumed to satisfy certain regularity conditions, namely, it has exactly $k$ ( $=\!0, 1, 2, \ldots $ ) quadratic mean derivatives (q.m.d.). The quality of the estimation is measured by the mean squared error (MSE). Here the asymptotic results of the mean squared error are established. We found that the optimal bandwidth depends on the $(2k+1)$ th mixed partial derivatives of the autocovariance function along the diagonal of the unit square. Simulation results for the model of $k$ th order integrated Brownian motion error are given in order to assess the effect of the regularity of this error process on the performance of the kernel estimator.     

Effect of outliers on the estimation of parameters

Summary The estimation of parameter in the type of distributionf(x)=b x ^{–1 /b} exp (–x ^b (/b),x>0, is considered, when several outliers of the type , ,r=1,2, ...,k, are present in the data. The estimates of as well as of 's are put in the closed form. Special cases, Weibull, Gamma and Exponential are considered for the case of single outlier. Actual estimates are calculated from the generated samples of size 2 and 3 for the Weibull and Exponential.     

Asymptotic efficiencies of spacings tests for goodness of fit

Tests based on higher-order orm-step spacings have been considered in the literature for the goodness of fit problem. This paper studies the asymptotic distribution theory for such tests based on non-overlappingm-step spacings whenm, the length of the step, also increases with the sample sizen, to inifinity. By utilizing the asymptotic distributions under a sequence of close alternatives and studying their relative efficiencies, we try to answer a central question about the choice ofm in relation ton. Efficiency comparisons are made with tests based on overlappingm-step spacings, as well as corresponding chi-square tests.     

Asymptotic behaviour of near-maxima of Gaussian sequences

Let \((X_1,X_2,\ldots ,X_n)\) be a Gaussian random vector with a common correlation coefficient \(\rho _n,\,0\le \rho _n<1\) , and let \(M_n= \max (X_1,\ldots , X_n),\,n\ge 1\) . For any given \(a>0\) , define \(T_n(a)= \left\{ j,\,1\le j\le n,\,X_j\in (M_n-a,\,M_n]\right\} ,\,K_n(a)= \#T_n(a)\) and \(S_n(a)=\sum \nolimits _{j\in T_n(a)}X_j,\,n\ge 1\) . In this paper, we obtain the limit distributions of \((K_n(a))\) and \((S_n(a))\) , under the assumption that \(\rho _n\rightarrow \rho \) as \(n\rightarrow \infty ,\) for some \(\rho \in [0,1)\) .     

New Regionalism contested: some remarks in light of the case of the Mezzogiorno of Italy

This article attempts to re‐consider the debate that has recently developed around the so‐called New Regionalism with reference to the studies regarding the emergence of a ‘new’ competitive Mezzogiorno of Italy. The first two sections of the article are devoted to a critical analysis of the literature on the New Mezzogiorno. It is argued that this literature has, on the one hand, fruitfully called attention to the emerging experiences of regional development in the South of Italy; yet, on the other hand, in throwing positive light on local economic development in the South of Italy, it has underestimated the more troublesome phenomena that these experiences reveal, especially from the point of view of capital‐labour relations. The third section of the article is devoted to showing how the limits and contradictions of the new regionalist approach to local development are reflected in the new course of regional policy that has been embraced in Italy in recent years. Finally, in the concluding section, the article argues for a shift towards a critical approach to research on the Italian southern regions and local productive systems. L'article propose une relecture du débat qui s'est récemment développé autour du Nouveau Régionalisme,è partir des travaux concernant l'émergence d'un ‘nouveau’ Mezzogiorno compétitif en Italie. Les deux premières sections de l'article proposent une analyse critique de la littérature sur le Nouveau Mezzogiorno. D'un côté, celle‐ci a permis, de façon fructueuse, d'attirer l'attention sur l'émergence d'expériences de développement régional dans le Sud italien. De l'autre, en jetant une lumière positive sur le développement économique local dans le Sud de l'Italie, cette littérature a sous‐estimé les aspects les plus problématiques que ces expériences révèlent, en particulier du point de vue des relations entre capital et travail. La troisième partie montre combien le nouveau cours pris par les politiques régionales en Italie reflète les limites et les contradictions de l'approche néo‐régionaliste du développement local. En conclusion, l'article se penche sur la nécessité de développer une approche critique à la recherche sur les régions et les systèmes productifs locaux en Italie du Sud.     

Development Peculiarities of Peripheral Desert Settlements: The Case of Israel

Selected statistical time-series covering the 30-year period from 1965–94 were studied to determine general trends of both economic development and population growth of urban settlements in the Negev desert of Israel. The research indicated that in comparison with urban settlements located in central ‘non-desert’ districts of the country, peripheral desert localities tend to exhibit wider fluctuations of economic activity, unstable population growth, and an attenuation of general urbanization trends that manifest themselves elsewhere across the country. The research led to a set of analytical models designed to explain development peculiarities of peripheral desert settlements. In addition, several planning strategies were proposed, aimed at enhancing the socio-economic sustainability of existing settlements in peripheral desert areas and facilitating prospective urban development there. These include: (1) the establishment of development clusters consisting of urban settlements which share some essential interregional functions such as employment, educational, cultural, and recreational services and facilities; (2) the adoption of a system of progressive economic incentives to promote private investment in peripheral desert areas; and (3) stricter regulation of land use in the central, non-desert regions of the country. Although the present analysis was restricted to small and medium urban settlements in Israel, the mode of analysis and its practical applications can be useful for urban and regional planning elsewhere. Certaines périodes, sélectionnées par le moyen de statistiques et couvrant une tranche de 30 ans de 1965 à 1994, ont étéétudiées afin de déterminer les tendances générales du développement économique et de l'augmentation démographique des installations urbaines dans le désert du Negev en Israël. Cette recherche indique que, par rapport aux centres urbains situés dans les régions centrales ‘non-désert’ du pays, les localités désertiques périphériques ont tendance à faire preuve de changements d'activités économiques plus prononcés, d'une croissance démographique instable et d'une atténuation de la tendance vers l'urbanisation générale qui se révélent ailleurs dans le pays. Cette recherche a conduit à une série de modéles analytiques créés afin d'expliquer les particularités du développement des installations périphériques du désert. De plus, plusieurs stratégies de planification ont été proposées, dans le but d'augmenter la viabilité socio-économique des installations existantes dans les régions périphériques du désert et d'y faciliter le développement urbain futur. Celles-ci comprennent: (1) l'établissement de groupes de développement composés d'installations urbaines partageant certaines fonctions inter-régionales essentielles comme les services et aménagements pour l'emploi, l'éducation, la culture et les loisirs; (2) l'adoption d'un systéme d'encouragements économiques progressifs pour promouvoir les investissements privés dans les régions périphériques du désert; et (3) des réglementations plus strictes quant à l'utilisation des terres dans les régions centrales non désertiques du pays. Bien que l'analyse actuelle ait été limitée aux installations urbaines de petite et moyenne tailles en Israël, la méthode d'analyse et ses applications pratiques peuvent ? tre utiles pour la planification urbaine et régionale dans d'autres régions.